The fast-food company owns just under 50 percent of the unit. Bids are due next week and a number of private-equity firms are considering bids, the Journal reported. http://on.wsj.com/2jmINjh

Morgan Stanley is running the sale, the newspaper reported, citing one of the sources.

McDonald's — which last week agreed to sell the bulk of its China and Hong Kong business to state-backed conglomerate CITIC Ltd <0267.HK> and Carlyle Group LP <CG.O> — said in January last year that it was looking to sell a portion of its stake in the Japanese business.

"McDonald's Corp is continuing to explore a potential sale of a portion of its ownership in McDonald's Japan. There have been no decisions made at this time," company spokeswoman Terri Hickey said in an email.